Yes, it is possible. They can check what websites she browses, instant
messages and broadcasts (Twitter, Identi.ca, etc.).

Is it likely? It depends on the administrator and the policies of her
employer. Right now the sky is the limit for snooping and the boss is within
his rights, legally. It is the company's equipment and their time.
Ethically, it is another question.

My own opinion is that this is going to increase, not decrease. Governments
are doing it and there is even talk of them monitoring your behaviour for
mental problems and cruising the streets to listen in and even view what it
going on in your home using equipment like that used to look through
clothing at airports. Companies are producing vans to do this as I write.
The NSA in the US is building huge sites in the desert to store and monitor
all electronic transmissions. Foreign governments will et in on the act to
trade secrets with the big boys as everyone wants a piece of the action and
besides we will soon have one world government.